arXiv subjects

Paul J. Steinhardt

Publications and source records attributed to Paul J. Steinhardt.

At least 19 recordsLinked to original sources

arXiv2026

Anti-Ultralocality and Plateau Models of Inflation

Anti-ultralocality refers to the growth of spatial gradient terms relative to velocity terms in the coupled Einstein--scalar field equations. It is a characteristic feature of decelerated expansion before the onset of inflation. Previous numerical relativity studies have shown that anti-ultralocality prevents the onset of inflation in models with power-law inflaton potentials. In this paper, we show that models with plateau-shaped inflaton potentials, which are considered to be the simplest way to generate a tensor-to-scalar ratio below current observational upper limits, are especially vulnerable to anti-ultralocality effects. The reasons are the flatness of the plateau and the energy density gap of $\sim 10$ orders of magnitude between the Planck density and the plateau potential energy. To study the problem, we develop a protocol for assessing the viability of inflationary models in general, and we apply it to a plateau potential using a previously validated numerical relativity code. We find that, starting from generic initial conditions, the growth of gradient terms in the Einstein equations relative to non-gradient terms either prevents inflation from lasting for enough $e$-folds or triggers a phase of quantum runaway. We show that the fine-tuning of initial conditions necessary to avoid these issues becomes more severe as the energy scale of inflation is made smaller, disfavoring common approaches for reducing the tensor-to-scalar ratio.

gr-qc↗

arXiv2026

Causal Horizons, Geodesic Completeness and Stability in Slow Contraction Cosmology

We show that cosmological models with a semi-infinite phase of slow contraction (ekpyrosis) possess a combination of properties that can address several fundamental problems in cosmology, otherwise faced in contracting de Sitter phases or standard big bang expansion. In particular, slow contraction admits a stable past attractor asymptoting to Minkowski space, as well as a stable, flat, homogeneous, and isotropic future attractor with negligible Weyl curvature (and, therefore, negligible gravitational entropy). In bouncing cosmologies, this contracting attractor is terminated by a smooth, non-singular bounce that transforms the attractor properties at the end of contraction into the initial conditions for the subsequent expanding phase. Cosmologies incorporating a slow contraction phase have no particle horizon and therefore avoid the causal horizon problem. The past Minkowski attractor also generates an initial spectrum of vacuum-like quantum fluctuations on all wavelengths. Moreover, because the averaged expansion rate along past-directed geodesics is non-positive, models incorporating a semi-infinite phase of slow contraction also evade the Borde,Guth and Vilenkin theorem and are past geodesically complete. By contrast, contracting de Sitter space possesses a finite particle horizon and becomes unstable in the presence of scalar fields, matter, or radiation.

gr-qc↗

arXiv2026

Structural and physical properties of gyromorphs and disordered stealthy hyperuniform media

Disordered stealthy hyperuniform materials combine liquid-like statistical isotropy with crystal-like homogeneity, suppressed density fluctuations at large length scales, bounded holes, and an isotropic structure factor that vanishes for a finite range of wavevectors. This combination yields unusual physical properties, including optical transparency, effective delocalization, ultrafast spreadability, optimal conductivity, and complete isotropic photonic bandgaps. Gyromorphs, point patterns whose structure factor includes rings of Bragg-like peaks arranged with discrete $G$-fold rotational symmetry, were recently introduced as counterexamples: disordered media that can somehow achieve the same physical properties, in some cases with higher performance, without stealthiness or hyperuniformity. In this paper, we resolve the puzzle of how gyromorphs fit consistently with the stealthy hyperuniform studies. We first show that gyromorphs are actually hyperuniform and, in the large-$G$ limit where they become nearly isotropic, belong to the weakest form of hyperuniformity, known as Class III. Thus, gyromorphs should have comparatively degraded physical properties compared to stealthy hyperuniform media, which belong to the strongest form of hyperuniformity, known as Class I. We verify this expectation using the rigorous spectral Green's matrix method for the calculation of the density of states (DOS) and Purcell factors in large arrays of electric dipoles. We find that gyromorphs display size-dependent pseudogaps richly populated by localized states rather than smooth band gaps like those found for highly stealthy hyperuniform materials or in deterministic structures such as Vogel spiral and triangular lattices. Furthermore, we predict similar disorder-induced degradation relative to stealthy hyperuniformity with regard to transparency, spreadability and diffusion properties.

physics.optics↗

arXiv2026

Inferring stealthy hyperuniform correlations from quantum transport

Stealthy hyperuniform disordered systems exhibit strongly suppressed long-wavelength fluctuations, producing correlated disorder with unusual consequences for wave propagation. A central quantity characterizing these systems is the stealthiness parameter $χ$, which controls the range of excluded Fourier components in the disorder spectrum. However, in realistic settings, the microscopic disorder configuration may not be directly accessible, making it challenging to determine $χ$ from structural information alone. Here, we propose a conductance-based inverse protocol to recover stealthy hyperuniform correlations from transport data. As a proof of concept, we study spinless fermions in a one-dimensional tight-binding chain connected to clean semi-infinite leads, with on-site disorder generated by imposing a stealthy spectrum $S(k)=Θ(|k|-K)$, where $K=2πχ$. The energy-dependent transmittance is computed using a recursive Green's function method and compared with target spectra through a misfit function defined over an energy window. We show that the position of the sharp drop separating high- and low-transmittance regions is strongly controlled by $χ$, while the disorder strength $W$ mainly affects the absolute magnitude of the transmittance. As a result, the misfit function displays a clear minimum close to the target stealthy parameter. Our results demonstrate that transmittance spectra can serve as fingerprints of stealthy hyperuniform disorder, providing a practical route to infer correlated-disorder parameters from transport measurements.

cond-mat.mes-hall↗

arXiv2026

Towards stealthy hyperuniform networks with optimal isotropic complete photonic band gaps using a novel inverse design procedure

We present a two-stage inverse design procedure for producing disordered stealthy hyperuniform trivalent photonic networks in two dimensions with isotropic complete photonic band gaps (PBGs) blocking light regardless of direction or polarization (TE or TM) over a wide frequency range. Most ordinary disordered systems fail to maintain complete PBGs as system size increases. The only known exceptions that remain open in the largest simulations have been generated by mapping stealthy hyperuniform point patterns into trivalent networks. However, the resulting networks are not truly stealthy hyperuniform two-phase media. Although their PBGs remain open, they are relatively narrow due to limited overlap between the TE and TM band gaps and broad band tails caused by localized defect states. By contrast, our two-stage inverse design aims to make the final network itself stealthy hyperuniform, achieving unprecedented near-optimal overlap between the TE and TM band gaps and a small defect state density at the band edges. We obtain not only single realizations with large PBGs, but a striking homogeneity across a large ensemble, effectively probing a network with 100,000 vertices. This ensemble-based band gap is comparable in width to the complete PBG of an anisotropic honeycomb photonic crystal with the same network parameters and nearly an order of magnitude wider than the previously widest known isotropic complete PBGs. Our designs can be fabricated using additive manufacturing, offering new pathways to manipulate electromagnetic waves for photonic technologies.

physics.optics↗

arXiv2026

Two-dimensional stealthy hyperuniform polycrystalline disk packings

Polycrystals consist of grains of local crystalline order separated by grain boundaries. Their structure is not hyperuniform, even though perfect crystals are, because polycrystals consist of randomly sized and oriented grains that generate appreciable long-wavelength density fluctuations. In this paper, we use a collective-coordinate optimization procedure to generate two-dimensional polycrystalline packings composed of identical disks arranged in a pattern that is ultradense, stealthy, and hyperuniform (hereafter named SHU). We compare them with polycrystalline disk packings obtained via a modified Lubachevsky--Stillinger rapid compression algorithm (hereafter named LS), a molecular dynamics protocol that serves as a standard reference model describing realistic, nonhyperuniform polycrystalline microstructures. We carry out an extensive comparison of polycrystalline SHU and LS packings that includes differences in two-point statistics, grain size, specific surface area, diffusion spreadability, and optical response as quantified by the imaginary part of the effective dynamic dielectric constant. We find that the polycrystalline SHU packings exhibit a distinctive grain-size distribution, a consequence of long-range correlations between different grains that is absent in the nonhyperuniform case. Within the nonlocal strong-contrast expansion, we confirm that polycrystalline SHU packings made of dielectric material are perfectly transparent to electromagnetic waves at small wave vectors, in contrast to LS packings. Moreover, polycrystalline SHU packings offer enhanced diffusion spreadability. Although polycrystalline SHU packings are not expected to form spontaneously in nature, they may be created for applications as metamaterials via nanolithography or 3D printing that take advantage of their distinctive optical and transport properties.

cond-mat.mtrl-sci↗

arXiv2026

Particle Production by Time-Varying Dark Energy and the End of Cosmic Expansion

We consider various possible consequences of time-varying dark energy due to a quintessence scalar field whose energy density is partially converted to particles as the field evolves down its potential. This particle production acts as a source of thermal friction on the field that can make it difficult to distinguish whether dark energy is due to a radiating field rolling down a steep potential, a purely self-interacting field moving down a flatter potential, or a cosmological constant. By reducing the acceleration of the scalar field, thermal friction increases the amount of accelerated expansion and can cause a sizable bump in the quintessence equation of state. We take special interest in the case where a steep potential rapidly changes from positive to negative as the field evolves, resulting in the end of cosmic expansion and the beginning of contraction. Even in this case, we find that thermal friction lengthens the period of accelerated expansion and consequently delays the end of cosmic expansion, making it challenging to detect the impending transition to contraction using conventional cosmological tests. However, particle production can also provide alternative avenues for detection by generating a background of thermal dark radiation, partly comprised of neutrinos or other particles, whose energy density exceeds the remnant photon energy density.

gr-qc↗

arXiv2026

Hyperuniformity of Weighted Particle Systems

Hyperuniform particle arrangements are characterized by a local number variance that grows more slowly than the volume of the observation window. We generalize this concept to describe particle systems in which particles carry weights: internal degrees of freedom such as scalars, vectors, pseudovectors, directors, tensors, or extrinsic local attributes. Our generalization extends hyperuniformity from fluctuations in particle positions to fluctuations in the spatial distribution of weights. We derive generalized weighted pair correlation, autocovariance, and spectral functions, and show their relation to the local variance in weighted many-particle systems. Applying this formalism to bond-orientational ordered phases, dipolar liquid water, Voronoi-cell volumes, and certain ionic liquids, we demonstrate that hyperuniformity in the particle system does not necessarily translate to hyperuniformity of the weighted system. In fact, cases exist where a hyperuniform particle system becomes antihyperuniform when weighted, and others where nonhyperuniform or antihyperuniform particle systems yield hyperuniform weighted systems. This theoretical framework provides a road map for quantifying large-scale fluctuations in weighted many-particle systems, offering a powerful tool for identifying systems with novel physical properties.

cond-mat.stat-mech↗

arXiv2025

Holography vs. Scale Separation

In this work, we point out a contradiction between holography and scale-separated AdS (i.e. parametrically large mass gap) in string theory, making the standard assumption that the holographic CFT describes the IR degrees of freedom on a brane that decouple from gravity. We show that the CFT can only decouple from gravity if the scalar potential in the dual AdS satisfies a certain criterion. Namely, there must exist a scalar field trajectory that follows the gradient of the scalar potential to the asymptotic region of the scalar field space in which limit $\partial_ϕ\ln(V)\partial_ϕ\ln(Λ_s)\leq2/(d-2)$, where $Λ_s$ is the quantum gravity cut-off. This condition, which generically implies lack of scale-separation, is satisfied in the standard examples of AdS/CFT. However, proposed attempts at achieving scale separation, such as DGKT, employ scalar potentials that violate this condition. We therefore conclude that the CFT duals of DGKT vacua cannot exist in string theory. Barring fine-tuning, our conclusions apply to other Ricci-flat flux compactifications including the KKLT scenario which relies on scale separation to obtain a metastable de Sitter uplift.

hep-th↗

arXiv2025

Holographic Constraints on the String Landscape

We show that holography imposes strong and general constraints on scalar field potentials in the string landscape, determined by the asymptotic structure of the underlying spacetime. Applying these holographic consistency conditions, we identify broad classes of scalar potentials that are incompatible with a well-defined dual description. These include potentials with extended plateaus, excessively steep or shallow asymptotics, certain zero crossings, and specific alignments of stable AdS minima in moduli space. In particular, making the standard assumption that the CFT dual to a stable AdS vacuum must be realized as a worldvolume theory of a brane in string theory, we show that the brane selects an infinite-distance limit in moduli space where parametric scale separation is forbidden. Furthermore, the steepness and positivity of the potential are restricted in that infinite distance direction. We also find that requiring the validity of the effective theory in the future vacuum, a natural holographic criterion, automatically enforces the Trans-Planckian Censorship Conjecture (TCC) for classical cosmological solutions with positive potentials. Taken together, these constraints exclude the leading proposals to realize scale-separated AdS vacua and metastable de Sitter vacua in the string theory landscape such as DGKT and KKLT.

hep-th↗

arXiv2025

Effective delocalization in the one-dimensional Anderson model with stealthy disorder

We study analytically and numerically the Anderson model in one dimension with "stealthy" disorder, defined as having a power spectrum that vanishes in a continuous band of wave numbers. Motivated by recent studies on the optical transparency properties of stealthy hyperuniform layered media, we compute the localization length using a perturbative expansion of the self-energy. We find that, for fixed energy and small but finite disorder strength $W$, there exists for any finite length system a range of stealthiness $χ$ for which the localization length exceeds the system size. This kind of "effective delocalization" is the result of the novel kind of correlated disorder that spans a continuous range of length scales, a defining characteristic of stealthy systems. Unlike uncorrelated disorder, for which the localization length $ξ$ scales as $W^{-2}$ to leading order for small W, the leading order terms in the perturbation expansion of $ξ$ for stealthy disordered systems vanish identically for a progressively large number of terms as $χ$ increases such that $ξ$ scales as $W^{-2n}$ with arbitrarily large $n$. Moreover, we support our analytical results with numerical simulations. Our results introduce stealthy disorder into quantum tight-binding models and show that enforcing a low-$k$ spectral gap markedly alters the scattering landscape, enabling localization lengths that exceed the system size at fixed disorder strength. Since this mechanism relies only on the spectral properties of the disorder, it carries over directly to photonic and phononic wave systems.

cond-mat.dis-nn↗

arXiv2025

Quantifying when hyperuniformity of a many-particle system leads to uniformity across length scales

Hyperuniform systems are distinguished by an unusually strong suppression of large-scale density fluctuations and, consequently, display a high degree of uniformity at the largest length scales. In some cases, however, enhanced uniformity is expected to be present even at intermediate and possibly small length scales. There exist three different classes of hyperuniform systems, where class I and class III are the strongest and weakest forms, respectively. We utilize the local number variance $σ_N^2(R)$ associated with a window of radius $R$ as a diagnostic to quantify the approach to the asymptotic large-$R$ hyperuniform scaling of a variety of class I, II, and III systems. We find, for all class I systems we analyzed, including crystals, quasicrystals, disordered stealthy hyperuniform systems, and the one-component plasma, a faster approach to the asymptotic scaling of $σ_N^2(R)$, governed by corrections with integer powers of $1/R$. Thus, we conclude this represents the highest degree of effective uniformity from small to large length scales. Class II systems, such as Fermi-sphere point processes, are characterized by logarithmic $1/\ln(R)$ corrections and, consequently, a lower degree of local uniformity. Class III systems, such as perturbed lattice patterns, present an asymptotic scaling of $1/R^α$, $0 < α< 1$, implying, curiously, an intermediate degree of local uniformity. In addition, our study provides insight into when experimental and numerical finite systems are representative of large-scale behavior. Our findings may thereby facilitate the design of hyperuniform systems with enhanced physical properties arising from local uniformity.

cond-mat.stat-mech↗

arXiv2025

Instant Folded Strings, Dark Energy and a Cyclic Bouncing Universe

We present a wholly self-consistent, complete cyclic bouncing cosmology based on components drawn from string theory and constructed in a way that is under perturbative control throughout (e.g., with temperature much less than the string scale and string coupling $g_s \ll 1$ at all times). The cyclic evolution is governed by standard dilaton-gravity in $(3+1)$-dimensions with a perturbatively generated potential and a coupling between the dilaton and a second field that becomes massless at $ϕ= ϕ_{ESP}$, resulting in an enhanced symmetry point (ESP) that prevents the dilaton from running all the way to zero coupling. A central role is played by instant folded strings (IFSs) - fundamental strings with the unusual property of being much lighter than the string mass while extending far beyond the string length, and violating the Null Energy Condition (NEC). IFSs are produced classically when the string coupling grows with time, which occurs at two critical points in each cycle. In turn, they fulfill a dual function: enabling cosmological bounces and initiating transient epochs of dark-energy domination that naturally transition into slow contraction. The resulting cosmology eliminates the cosmic singularity and multiverse problems of big bang inflationary models and robustly predicts time-varying IFS-induced dark energy and the absence of primordial B-mode polarization in the cosmic microwave background.

gr-qc↗

arXiv2025

Transparency versus Anderson localization in one-dimensional disordered stealthy hyperuniform layered media

We present numerical simulations of disordered stealthy hyperuniform layered media ranging up to 10,000 thin slabs of high-dielectric constant separated by intervals of low dielectric constant that show no apparent evidence of Anderson localization of electromagnetic waves or deviations from transparency for a continuous band of frequencies ranging from zero up to some value $ω_T$. The results are consistent with the strong-contrast formula including its tight upper bound on $ω_T$ and with previous simulations on much smaller systems. We utilize a transfer matrix method to compute the Lyaponov exponents, which we show is a more reliable method for detecting Anderson localization by applying it to a range of systems with common types of disorder known to exhibit localization, such as perturbed periodic lattices. The Lyaponov exponents for these systems with ordinary disorder show clear evidence of localization, in contrast to the cases of perfectly periodically spaced slabs and disordered stealthy hyperuniform layered systems. As with any numerical study, one should be cautious about drawing definitive conclusions. There remains the challenge of determining whether one-dimensional disordered stealthy hyperuniform layered media possess a finite localization length on some scale much larger than our already large system size or, alternatively, are exceptions to the standard Anderson localization theorems.

cond-mat.dis-nn↗

arXiv2025

Dynamical properties of particulate composites derived from ultradense stealthy hyperuniform sphere packings

Stealthy hyperuniform (SHU) many-particle systems are distinguished by a structure factor that vanishes not only at zero wavenumber (as in ``standard'' hyperuniform systems) but also across an extended range of wavenumbers near the origin. We generate disordered SHU packings of identical and `nonoverlapping' spheres in $d$-dimensional Euclidean space using a modified collective-coordinate optimization algorithm that incorporates a soft-core repulsive potential between particles in addition to the standard stealthy pair potential. These SHU packings are ultradense, spanning a broad spectrum of structures depending on the stealthiness parameter $χ$. We consider two-phase media composed of hard particles derived from ultradense SHU packings embedded in a matrix phase, with varying stealthiness parameter $χ$ and packing fractions $ϕ$. Our main objective is the estimation of the dynamical physical properties of such two-phase media, namely, the effective dynamic dielectric constant and the time-dependent diffusion spreadability, which is directly related to nuclear magnetic relaxation in fluid-saturated porous media. We show through spreadability that two-phase media derived from ultradense SHU packings exhibit faster interphase diffusion due to the higher packing fractions achievable compared to media obtained without soft-core repulsion. The imaginary part of the effective dynamic dielectric constant of SHU packings vanishes at a small wavenumber, implying perfect transparency for the corresponding wavevectors. We also obtain cross-property relations between transparency characteristics and long-time behavior of the spreadability for such two-phase media. Our results demonstrate that disordered two-phase media derived from ultradense SHU packings exhibit advantageous transport and optical behaviors of both theoretical and experimental significance.

cond-mat.soft↗

arXiv2025

Optimal parameterizations for observational constraints on thawing dark energy

Time-varying dark energy is often modeled in observational analyses through generic parameterizations of its equation of state $w(z)$, which typically use two free parameters $\{w_0, w_a\}$ to span a broad range of behaviors as a function of redshift. However, this broad range of behaviors can only approximately capture the dynamics of any given microphysical theory of dark energy. A complementary approach is to use targeted parameterizations designed to model specific classes of dynamical dark energy with greater precision. Focusing on the class of thawing dark energy, we quantify and compare the precision with which nineteen generic and targeted parameterizations can capture the dynamics of physically motivated thawing quintessence theories. We find that a targeted parameterization derived from a Padé expansion of $w$ is the most reliable of these, producing accurate reconstructions of $w(z)$, the expansion history $H(z)$, and cosmological parameters such as $H_0$ and $Ω_m$ for a broad range of microphysical theories.

astro-ph.CO↗

arXiv2024

Moduli Axions, Stabilizing Moduli and the Large Field Swampland Conjecture in Heterotic M-Theory

We compute the potential energy for the dilaton, complex structure and Kahler moduli and search of realistic vacua of heterotic M-theory compactified on Calabi-Yau threefolds. We present a protocol for deriving the potential that combines the non-perturbative complex structure, gaugino condensate and worldsheet instanton superpotentials in theories in which the hidden sector contains an anomalous $U(1)$ structure group. The Green-Schwarz anomaly cancellation induces inhomogeneous axion transformations for the imaginary components of the dilaton and Kahler modulus. Using this protocol we obtain explicit examples in which potential has a global minimum at negative or zero vacuum density or a metastable minimum with positive vacuum density. In all three cases, the dilaton, Kahler modulus and associated axion moduli are completely stabilized. Finally, we show that, for any of these vacua, the potential energy satisfies the large scalar field Swampland conjecture.

hep-th↗

arXiv2024

Hyperuniformity Classes of Quasiperiodic Tilings via Diffusion Spreadability

Hyperuniform point patterns can be classified by the hyperuniformity scaling exponent $α> 0$, that characterizes the power-law scaling behavior of the structure factor $S(\mathbf{k})$ as a function of wavenumber $k\equiv|\mathbf{k}|$ in the vicinity of the origin, e.g., $S(\mathbf{k})\sim|\mathbf{k}|^α$ in cases where $S(\mathbf{k})$ varies continuously with $k$ as $k\rightarrow0$. In this paper, we show that the spreadability is an effective method for determining $α$ for quasiperiodic systems where $S(\mathbf{k})$ is discontinuous and consists of a dense set of Bragg peaks. We first transform quasiperiodic and limit-periodic point patterns into two-phase media by mapping them onto packings of identical nonoverlapping disks, where space interior to the disks represents one phase and the space in exterior to them represents the second phase. We then compute the spectral density of the packings, and finally compute and fit the long-time behavior of their excess spreadabilities. Specifically, we show that the excess spreadability can be used to accurately extract $α$ for the 1D limit-periodic period doubling chain and the 1D quasicrystalline Fibonacci chain to within $0.02\%$ of the analytically known exact results. Moreover, we obtain a value of $α= 5.97\pm0.06$ for the 2D Penrose tiling, which had not been computed previously. We also show that one can truncate the small-$k$ region of the scattering information used to compute the spreadability and still obtain an accurate value of $α$. The methods described here offer a simple way to characterize the large-scale translational order present in quasicrystalline and limit-periodic media in any space dimension that are self-similar. Moreover, the scattering information extracted from these two-phase media encoded in the spectral density can be used to estimate their physical properties. (abridged)

cond-mat.stat-mech↗